Novel compounds in the hafnium nitride system: first principle study of their crystal structures and mechanical properties

Fan Tao; Zeng Qing-Feng; Yu Shu-Yin

doi:10.7498/aps.65.118102

Abstract

Motivated by exploring new high temperature ceramics which have excellent mechanical properties, we systematically search for all the stable compounds and their crystal structures in the binary Hf-N system by combining the evolutionary algorithm with first principle calculation. In addition to the well-known rock-salt HfN, we find five other novel compounds, i.e., Hf6N(R-3), Hf3N(P6322), Hf3N2(R-3m), Hf5N6(C2/m), and Hf3N4(C2/m). Then, their phonon frequencies are calculated so that the dynamical stabilities are known. Their high temperature thermodynamic stabilities are further confirmed and the Gibbs free energies are calculated in thequasi-harmonic approximation. All of these structures are thermodynamic stable when the temperature is lower than 1500 K. However, as temperature increases, the structuresHf5N6(C2/m) and Hf3N4(C2/m) become meta-stable. Meanwhile, some meta-stable structures, including Hf2N (P42/mnm), Hf4N3 (C2/m), Hf6N5(C2/m), Hf4N5(I4/m), Hf3N4 (I-43d), and Hf3N4 (Pnma), each of which has higher symmetry and lower formation enthalpy, are all listed. At the same time, our results of Hf3N4 testify that C2/m structure is stabler than Pnma and I-43d structures when the temperature is lower than 2000 K, which is different from the conclusion given by Bazhanov [Bazhanov D I, Knizhnik A A, Safonov A A, Bagatur'yants A A, Stoker M W, Korkin A A 2005 J. Appl. Phys. 97 044108]. The results also show that the difference in Gibbs free energy between C2/m and Pnma Hf3N4 structure decreases with temperature increasing. Thus, we speculate that the C2/m Hf3N4 transforms into Pnma Hf3N4 when the temperature is above 2000 K. The mechanical properties, including the elastic constant, bulk modulus, shear modulus, Young's modulus and hardness, are systematically investigated. The hardness first increases, reaching a maximum at Hf5N6 (21 GPa), and then decreases with increasing nitrogen content. Besides, Hf3N2 and Hf4N5 both exhibit relatively high hardness value of 19 GPa, while the hardness of HfN is 15 GPa. Finally, the electron densities of states and crystal orbital Hamilton populations are calculated so that the mechanic origins can be analyzed from the electronic structures of these phases. The crystal orbital Hamilton populations show that the strength of Hf-N covalent bonding increases with increasing nitrogen content, however, it has an exceptional peak for Hf3N2, which can be used to explain the relatively high hardness of this structure. Beside covalent bonding strength, structural vacancy can also affect their mechanical properties. It is concluded that the strong covalent bonding and low structural vacancy both can explain the good mechanical performance of Hf5N6.

Keywords:

Authors and contacts

1.
The International Center of Materials Design, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, China;
2.
Science and Technology on Thermostructural Composite Materials Laboratory, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, China

Corresponding author: Zeng Qing-Feng, qfzeng@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51372203, 51332004) and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. 3102015BJ(II) JGZ005).

References

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[29]	Lyakhov A O, Oganov A R, Valle M 2010 Comput. Phys. Commun. 181 1623
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[36]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[37]	Blchl P E 1994 Phys. Rev. B 50 17953
[38]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[39]	Wang S Q, Ye H Q 2003 J. Phys. Condens. Mat. 15 5307
[40]	Hill R 1952 Proc. Phys. Soc. London, Sect. A 65 349
[41]	Voigt W 1910 Lehrbuch der kristallphysik (Leipzig: B.G. Teubner) pp100
[42]	Reuss A 1929 Z. Angew. Math. Mech. 9 49
[43]	Chen X Q, Niu H, Li D, Li Y 2011 Intermetallics 19 1275
[44]	Ohodnicki Jr P, Cates N, Laughlin D, Mchenry M, Widom M 2008 Phys. Rev. B 78 144414
[45]	Morris A J, Grey C P, Needs R J, Pickard C J {2012 Phys. Rev. B 84 1894
[46]	Christensen A 1990 Acta Chem. Scand. 44 851
[47]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106
[48]	Shankar A R, Mudali U K, Chawla V, Chandra R 2013 Ceram. Int. 39 5175
[49]	Zaoui A, Bouhafs B, Ruterana P 2005 Mater. Chem. Phys. 91 108
[50]	Nagao S, Nordlund K, Nowak R {2006 Phys. Rev. B 73 144113
[51]	Patil S K R, Mangale N S, Khare S V, Marsillac S 2008 Thin Solid Films 517 824
[52]	Chen Z Q, Wang J, Li C M 2013 J. Alloys Compd. 575 137
[53]	Peter K 2003 Phys. Rev. Lett. 90 125501
[54]	Cowley R 1976 Phys. Rev. B 13 4877
[55]	Liu A Y, Wentzcovitch R M 1994 Phys. Rev. B 50 10362
[56]	Karki B B, Ackland G J, Crain J 1997 J. Phys. Condens. Mat. 9 8579
[57]	Yang Q, Lengauer W, Koch T, Scheerer M, Smid I 2000 J. Alloys Compd. 309 L5
[58]	Gupta D C, Chauhan M, Bhat I H {2014 J. Appl. Phys. 1591 36
[59]	Chung H Y, Weinberger M B, Yang J M, Tolbert S H, Kaner R B 2008 Appl. Phys. Lett. 92 261904
[60]	Jacobson B E, Nimmagadda R, Bunshah R F 1979 Thin Solid Films 63 333
[61]	Deringer V L, Tchougreff A L, Richard D 2011 J. Phys. Chem. A 115 5461
[62]	Dronskowski R, Bloechl P E 1993 J. Phys. Chem. 97 8617

Cited By

[1]	Zhang L L, Fu Q G, Li H J {2015 Mater. Chin. 34 675 (in Chinese) [张磊磊, 付前刚, 李贺军 2015 中国材料进展 34 675]
[2]	Xie Y, Cheng L, Li L, Mei H, Zhang L 2013 J. Eur. Ceram. Soc. 33 1701
[3]	Li H, Zhang L, Cheng L, Wang Y, Yu Z, Huang M, Tu H, Xia H 2008 J. Mater. Sci. 43 2806
[4]	Huang S H, Liu J 2014 Chin. Phys. B 23 058105
[5]	Wang C L, Yu B H, Huo H L, Chen D, Sun H B 2009 Chin. Phys. B 18 1248
[6]	Zhao L K, Zhao E J, Wu Z J 2013 Acta Phys. Sin. 62 046201 (in Chinese) [赵立凯, 赵二俊, 武志坚 2013 62 046201]
[7]	Zhang G T, Bai T T, Yan H Y, Zhao Y R 2015 Chin. Phys. B 24 106104
[8]	Peng J H, Zeng Q F, Xie C W, Zhu K J, Tan J H {2015 Acta Phys. Sin. 64 236102 (in Chinese) [彭军辉, 曾庆丰, 谢聪伟, 朱开金, 谭俊华 2015 64 236102]
[9]	Zhang M G, Yan H Y, Zhang G T, Wang H 2012 Chin. Phys. B 21 076103
[10]	Pu C Y, Zhou D W, Bao D X, Lu C, Jin X L, Su T C, Zhang F W 2014 Chin. Phys. B 23 026201
[11]	Li X F, Zhai H C, Fu H Z, Liu Z L, Ji G F 2011 Chin. Phys. B 20 093101
[12]	Zhao W J, Wang Y X 2009 Chin. Phys. B 18 3934
[13]	Wang J, Li C M, Ao J, Li F, Chen Z Q 2013 Acta Phys. Sin. 62 087102 (in Chinese) [王瑨, 李春梅, 敖靖, 李凤, 陈志谦 2013 62 087102]
[14]	Xun X C 2008 M.S. Dissertation (Changchun: Jilin University) (in Chinese) [荀显超 2008 硕士学位论文 (长春: 吉林大学)]
[15]	Santecchia E, Hamouda A, Musharavati F, Zalnezhad E, Cabibbo M, Spigarelli S 2015 Ceram. Int. 41 10349
[16]	Patsalas P, Kalfagiannis N, Kassavetis S 2015 Materials 8 3128
[17]	Sue J, Chang T {1995 Surf. Coat. Technol. 76 61
[18]	Bringans R D, Hchst H 1984 Phys. Rev. B 30 5416
[19]	Benia H M, Guemmaz M, Schmerber G, Mosser A, Parlebas J C 2002 Appl. Surf. Sci. 200 231
[20]	Chen X J, Struzhkin V V, Wu Z, Somayazulu M, Qian J, Kung S, Christensen A N, Zhao Y, Cohen R E, Mao H K 2005 Proc. Natl. Acad. Sci. U.S.A. 102 3198
[21]	Zhao E, Wu Z 2008 J. Solid State Chem. 181 2814
[22]	Reza M, Lech A T, Miao X, Weaver B E, Yeung M T, Tolbert S H, Kaner R B 2011 Proc. Natl. Acad. Sci. U.S.A. 108 10958
[23]	Yamanaka S, Hotehama K I, Kawaji H 1998 Nature 392 580
[24]	Gasch M, Ellerby D, Irby E, Beckman S, Gusman M, Johnson S 2004 J. Mater. Sci. 39 5925
[25]	Johansson B O, Sundgren J E, Helmersson U, Hibbs M K 1984 Appl. Phys. Lett. 44 670
[26]	Seo H S, Lee T Y, Wen J G, Petrov I, Greene J E, Gall D 2004 J. Appl. Phys. 96 878
[27]	Zerr A, Gerhard M, Ralf R 2003 Nat. Mater. 2 185
[28]	Bazhanov D I, Knizhnik A A, Safonov A A, Bagatur'yants A A, Stoker M W, Korkin A A 2005 J. Appl. Phys. 97 044108
[29]	Lyakhov A O, Oganov A R, Valle M 2010 Comput. Phys. Commun. 181 1623
[30]	Oganov A R, Glass C W 2006 J. Chem. Phys. 124 244704
[31]	Oganov A R, Lyakhov A O, Mario V 2011 Acc. Chem. Res. 44 227
[32]	Oganov, Artem R 2011 Modern Methods of Crystal Structure Prediction (New York: Wiley-VCH) pp147
[33]	Hohenberg P, Kohn W 1964 Phys. Rev. 136 864
[34]	Kohn W, Sham L J 1965 Phys. Rev. 140 1133
[35]	Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[36]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[37]	Blchl P E 1994 Phys. Rev. B 50 17953
[38]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[39]	Wang S Q, Ye H Q 2003 J. Phys. Condens. Mat. 15 5307
[40]	Hill R 1952 Proc. Phys. Soc. London, Sect. A 65 349
[41]	Voigt W 1910 Lehrbuch der kristallphysik (Leipzig: B.G. Teubner) pp100
[42]	Reuss A 1929 Z. Angew. Math. Mech. 9 49
[43]	Chen X Q, Niu H, Li D, Li Y 2011 Intermetallics 19 1275
[44]	Ohodnicki Jr P, Cates N, Laughlin D, Mchenry M, Widom M 2008 Phys. Rev. B 78 144414
[45]	Morris A J, Grey C P, Needs R J, Pickard C J {2012 Phys. Rev. B 84 1894
[46]	Christensen A 1990 Acta Chem. Scand. 44 851
[47]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106
[48]	Shankar A R, Mudali U K, Chawla V, Chandra R 2013 Ceram. Int. 39 5175
[49]	Zaoui A, Bouhafs B, Ruterana P 2005 Mater. Chem. Phys. 91 108
[50]	Nagao S, Nordlund K, Nowak R {2006 Phys. Rev. B 73 144113
[51]	Patil S K R, Mangale N S, Khare S V, Marsillac S 2008 Thin Solid Films 517 824
[52]	Chen Z Q, Wang J, Li C M 2013 J. Alloys Compd. 575 137
[53]	Peter K 2003 Phys. Rev. Lett. 90 125501
[54]	Cowley R 1976 Phys. Rev. B 13 4877
[55]	Liu A Y, Wentzcovitch R M 1994 Phys. Rev. B 50 10362
[56]	Karki B B, Ackland G J, Crain J 1997 J. Phys. Condens. Mat. 9 8579
[57]	Yang Q, Lengauer W, Koch T, Scheerer M, Smid I 2000 J. Alloys Compd. 309 L5
[58]	Gupta D C, Chauhan M, Bhat I H {2014 J. Appl. Phys. 1591 36
[59]	Chung H Y, Weinberger M B, Yang J M, Tolbert S H, Kaner R B 2008 Appl. Phys. Lett. 92 261904
[60]	Jacobson B E, Nimmagadda R, Bunshah R F 1979 Thin Solid Films 63 333
[61]	Deringer V L, Tchougreff A L, Richard D 2011 J. Phys. Chem. A 115 5461
[62]	Dronskowski R, Bloechl P E 1993 J. Phys. Chem. 97 8617

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